Problem: There is a light source on the plane. This source is so small that it can be represented as point. The light source is moving from point (a, s_y) to the (b, s_y) (s_y < 0) with speed equal to 1 unit per second. The trajectory of this light source is a straight segment connecting these two points. 

There is also a fence on OX axis represented as n segments (l_i, r_i) (so the actual coordinates of endpoints of each segment are (l_i, 0) and (r_i, 0)). The point (x, y) is in the shade if segment connecting (x,y) and the current position of the light source intersects or touches with any segment of the fence.

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You are given q points. For each point calculate total time of this point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y).

Input

First line contains three space separated integers s_y, a and b (-10^9 ≤ s_y < 0, 1 ≤ a < b ≤ 10^9) — corresponding coordinates of the light source.

Second line contains single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — number of segments in the fence.

Next n lines contain two integers per line: l_i and r_i (1 ≤ l_i < r_i ≤ 10^9, r_{i - 1} < l_i) — segments in the fence in increasing order. Segments don't intersect or touch each other.

Next line contains single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — number of points to check.

Next q lines contain two integers per line: x_i and y_i (1 ≤ x_i, y_i ≤ 10^9) — points to process.

Output

Print q lines. The i-th line should contain one real number — total time of the i-th point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y). The answer is considered as correct if its absolute of relative error doesn't exceed 10^{-6}.

Example

Input

-3 1 6
2
2 4
6 7
5
3 1
1 3
6 1
6 4
7 6


Output

5.000000000000000
3.000000000000000
0.000000000000000
1.500000000000000
2.000000000000000

Note

  * The 1-st point is always in the shade; 
  * the 2-nd point is in the shade while light source is moving from (3, -3) to (6, -3); 
  * the 3-rd point is in the shade while light source is at point (6, -3). 
  * the 4-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and at point (6, -3); 
  * the 5-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and from (5.5, -3) to (6, -3); 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
const int N = 1000005;
const double eps = 1e-9;
int n, m, a[N], b[N], ans, Q;
double l[N], r[N], sum[N];
int main() {
  register int sy, i, u, v;
  register double x, y, a, b;
  scanf("%d%d%d%d", &sy, &u, &v, &n), a = u, b = v;
  for (i = 1; i <= n; ++i)
    scanf("%d%d", &u, &v), l[i] = u, r[i] = v,
                           sum[i] = sum[i - 1] + r[i] - l[i];
  scanf("%d", &Q);
  while (Q--) {
    scanf("%d%d", &u, &v), x = u, y = v;
    const double p = (x * sy - a * y) / (sy - y),
                 q = (x * sy - b * y) / (sy - y);
    u = std::lower_bound(l + 1, l + 1 + n, p) - l,
    v = std::upper_bound(r + 1, r + 1 + n, q) - r - 1;
    register double s = sum[v] - sum[u - 1];
    if (u > 1 && r[u - 1] >= p) s += r[u - 1] - p;
    if (v < n && l[v + 1] <= q) s += q - l[v + 1];
    s < eps ? puts("0.000000000") : printf("%.9f\n", (b - a) * s / (q - p));
  }
  return 0;
}